There does seem to be a problem:
sage: k = 61*2^88+1 ; k
18878585599102049192211644417
sage: k.is_prime()
True
sage: k.factor()
18878585599102049192211644417
sage: k == 61*2^88+1
True
sage: GF(k)
Finite Field of size 18878585599102049192211644417
On Saturday, 2 April 2022 at 6:55:44 pm UTC+11 bea...@gmail.com wrote:
> It seems this number is a prime number and 18878585599102049192211644417 =
> 61*2^88+1 is not a factorization of the number. Hence, everything is fine.
> Am I missing something here?
>
> cheers,
> Andry
>
> Le sam. 2 avr. 2022 à 02:33, carlos ortiz <pep...@gmail.com> a écrit :
>
>> The number:
>>
>> 18878585599102049192211644417 = 61*2^88+1
>>
>> but in sage:
>>
>> k=ZZ(18878585599102049192211644417)
>>
>> k.is_prime()
>>
>> True
>>
>> k.factor()
>>
>> 18878585599102049192211644417
>>
>> F = FiniteField(18)
>>
>> raise ValueError("the order of a finite field must be a prime power")
>>
>>
>> Howeve,
>>
>> F=FiniteField(18878585599102049192211644417)
>>
>> F
>>
>> Finite Field of size 18878585599102049192211644417
>>
>> The above functions generate error for this number
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> --
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>> .
>>
>
>
> --
> Andry Nirina Rabenantoandro, PhD.
>
>
>
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